<p> Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. </p><p> This dissertation uses a systematic procedure for constructing geometric integrators &mdash; known as variational integration &mdash; to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically <i>multistep methods.</i> Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. </p><p> These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.</p>

<p>Plasma-based particle acceleration holds the promise to make the applications that revolve around accelerators more affordable. The central unifying theme of this dissertation is the modeling of certain non-linear and relativistic phenomena in plasma dynamics to devise mechanisms that benefit plasma-accelerators. Plasma acceleration presented here has two distinct flavors depending upon the accelerated particle mass which dictates the acceleration structure velocity and potential. The first deals with ion acceleration, where acceleration structure velocities are a significant fraction of the speed of light, with major applications in medicine. The second focusses on the acceleration of electrons and positrons for light-sources and colliders where the acceleration structures are wakefields with phase-velocities near the speed of light.</p> <p>The increasing Lorentz factor of the laser-driven electron quiver momentum forms the basis of Relativistically Induced Transparency Acceleration (RITA) scheme of ion acceleration. Lighter ions are accelerated by reflecting off a propagating acceleration structure, referred to as a snowplow, formed by the compression of ponderomotively driven critical layer electrons excited in front of a high intensity laser pulse in a fixed-ion plasma. Its velocity is controlled by tailoring the laser pulse rise-time and rising density gradient scale-length. We analytically model its induced transparency driven propagation with a 1-D model based on the linearized dispersion relation. The model is shown to be in good agreement with the weakly non-linear simulations. As the density compression rises into the strongly non-linear regime, the scaling law predictions remain accurate but the model does not exactly predict the RITA velocity or the accelerated ion-energy. Multi-dimensional plasma effects modify the laser radial envelope by self-focussing in the rising density gradient which can be integrated into our model and filamentation which is mitigated by a matched laser focal spot-size. We show that the critical layer motion in RITA compares favorably to the bulk-plasma motion driven by radiation pressure or collision-less shocks.</p> <p>Non-linear mixing of the laser, incident on and reflected off the propagating critical layer modulates its envelope affecting the acceleration structure velocity and potential, in the process setting up a feedback loop. For long pulses the envelope distortion grows with time, disrupting the accelerated ion-beam spectral shape. We model the Chirp Induced Transparency Acceleration (ChITA) mechanism that over- comes this effect by introducing decoherence through a frequency chirp in the laser. </p> <p>In a rising density gradient, the non-linearity of electron trajectories leads to the phase-mixing self-injection of electrons into high phase-velocity plasma wakefields. The onset of trapping depends upon the wake amplitude and the density gradient scale-length. This self-injection mechanism is also applicable to controlling the spuriously accelerated electrons that affect the beam-quality. </p> <p>Non-linear ion dynamics behind a train of asymmetric electron-wake excites a cylindrical ion-soliton similar to the solution of the cylindrical Korteweg-de Vries (cKdV) equation. This non-linear ion-wake establishes an upper limit on the repetition rate of the future plasma colliders. The soliton is excited at the non-linear electron wake radius due to the time-asymmetry of its radial fields. In a non-equilibrium wake heated plasma the radial electron temperature gradient drives the soliton. Its radially outwards propagation leaves behind a partially-filled ion-wake channel. </p> <p>We show positron-beam driven wakefield acceleration in the ion-wake channel. Optimal positron-wakefield acceleration with linear focussing fields is shown to require a matched hollow-plasma channel of a radius that depends upon the beam properties. </p> / Dissertation

I dagens samhälle används det mängder av antibiotika inom sjukvården. Detta medför att bakterier blir resistenta och mycket farliga. För att lösa detta behövs en ny innovativ lösning för att rengöra sår och infektioner. Den nya idén är att använd joniserad luft med bakteriedödande egenskaper. I denna rapport beskriver vi vårt arbete som blivande elektroingenjörer när vi tar fram elektroniken för en experimentprototyp för skapandet av kallplasma för jonisering av luft. / In today’s society antibiotics is used in high volume in health care. This causes the bacteria to become resistant and very dangerous. To address this need, a new innovative solution is needed to clean wounds and infections. The new idea is to use ionized air with germicidal properties. In this report, we describe our work as future electrical engineers when developing the electronics in an experimental prototype for the creation of cold plasma for air ionization.

Because the universe is primarily composed of plasma, the interaction of plasmas and magnetic fields is of great importance for astrophysics. In this dissertation, we investigate three magnetic instabilities and examine their possible effects on astrophysical objects. First, we model solar coronal structures as Double Beltrami states, which are the lowest energy equilibria of Hall magnetohydrodynamics. We find that these states can undergo a catastrophe with characteristics similar to those of a solar eruption, such as a flare or coronal mass ejection. We then investigate magnetic reconnection and particle acceleration in moderately magnetized relativistic pair plasmas with three-dimensional particle-in-cell simulations of a kinetic-scale current sheet. We find that in three dimensions the tearing instability produces a network of interconnected and interacting magnetic flux ropes. In its nonlinear evolution, the current sheet evolves toward a three-dimensional, disordered state in which the resulting flux rope segments contain magnetic substructure on kinetic scales and sites of temporally and spatially intermittent dissipation. We find that reconnection produces significant particle acceleration, primarily due to the electric field in the X-line regions between flux ropes; the resulting particle energy spectrum can extend to high Lorentz factors. We find that the highest energy particles are moderately beamed within. / text

Experiments on several tokamaks convincingly demonstrated that a deliberate seeding of selected impurities can have a positive effect on the plasma performance. On the one hand, a significant reduction of the head load on divertor plates, one of the main concerns by constructing a thermonuclear reactor, has been achieved due to the increase of edge radiation. On the other hand, in some devices impurity seeding has led to an improvement of the energy confinement and the so called radiation improved (RI) mode has been established with the same or even better confinement than in the H-mode. However, in order to make use of these positive impacts, the behaviour of seeded impurity has to be strictly controlled and such negative developments as the accumulation of impurity ions in the plasma core accompanied by a strong increase of the central radiation losses should be avoided. Plasma heating by radio-frequency (RF) waves has been proven to be a useful tool to control the behaviour of puffed impurities. In order to asses the prospective of impurity control by RF waves in larger devices and under reactor conditions, proper modelling approaches have been developed. One of the important parameters, which should be evaluated, is the averaged energy or temperature of heated impurity ions. The latter determines, in particular, the power transported to the main species, and, thus, the heating efficiency. Besides, the temperature of impurity ions characterizes the intensity of particle losses for heated impurities. An approach to compute the impurity temperature under such conditions is elaborated. It is based on the construction of a hierarchy of approximate solutions to the impurity heat balance equation and takes into account that the density and, thus, the heat conductivity of heated ion species can change by many orders of magnitude with the position in the plasma. The developed method has been incorporated into 1D transport code RITM. Coupled with the full wave code TORIC, the particle and heat balances for impurity and main plasma species provide a self-consistent approach to model the ion cyclotron resonance heating (ICRH) scenario. The modelling of various heating scenarios for several tokamaks displays the impacts of impurity heating on the heat and particles transport and heating efficiency. To investigate the possibility of impurity control at the large tokamak the experiment on selective impurity heating in the mode conversion H/D plasma was prepared and carried out in the tokamak JET.

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